Q1. ABC is a right – angled triangle with AB = 6 cm and BC = 8 cm. A circle with centre O has been inscribed inside ∆ABC. The radius of the circle is
(a) 1 cm
(b) 2 cm
(c) 3 cm
(d) 4 cm
Q2. The angles of a triangle are in the ratio 2 : 3 : 7. The measure of the smallest angle is
(a) 30°
(b) 60°
(c) 45°
(d) 90°
Q4. In a triangle ABC, BC is produced to D so that CD = AC. If ∠BAD = 111° and ∠ACB = 80°, then the measure of ∠ABC is:
(a) 31°
(b) 33°
(c) 35°
(d) 29°
Q5. If I be the incentre of ∆ABC and ∠B = 70° and ∠C = 50°, then the magnitude of ∠BIC is
(a) 130°
(b) 60°
(c) 120°
(d) 105°
Q6. If the three medians of a triangle are same, then the triangle is
(a) equilateral
(b) isosceles
(c) right – angled
(d) obtuse – angle
Q8. ST is a tangent to the circle at P and QR is a diameter of the circle. If ∠RPT = 50°, then the value of ∠SPQ is
(a) 40°
(b) 60°
(c) 80°
(d) 100°
Q9. In ∆ABC, if AD ⊥ BC, then AB^2+CD^2 is equal
(a) 2BD^2
(b) BD^2+AC^2
(c) 2 AC^2
(d) None of these
Q10. Given that: ∆ABC ~ ∆PQR, if (area ∆PQR)/(area ∆ABC)=256/441 and PR = 12 cm, then AC is equal to?
(a) 12√2 cm
(b) 15.5 cm
(c) 16 cm
(d) 15.75 cm
Solutions
S2. Ans.(a)
Sol. 2x + 3x + 7x = 180°
12x = 180°
x = 15°
Smaller = 2x
= 2 × 15°
= 30°
S3. Ans.(c)
Sol. ∠EOB = 30°
OE = OB = r
∠OEB = ∠OBE = 75°
∠CBE = 180° – 75°
= 105°
S6. Ans.(a)
Sol. Triangle is equilateral if the three medians of a triangle are same.
S7. Ans.(d)
Sol. ON = OY = r
∠ONY = ∠OYN = 50°
In ∆ONY
∠N + ∠Y + ∠O = 180°
50° + 50° + ∠O = 180°
(∠NOY = 80°)
OM = OY = r
In ∆OMY
∠M + ∠Y + ∠O = 180°
15° + 15° + ∠O = 180°
∠MOY = 150°
∠MON = 150° – 80°
= 70°
S10. Ans.(d)
Sol.(12/AC) = √(256/441)
(12/AC) = (16/21)
(3/AC) = (4/21)
AC = 63/4
AC = 15.75 cm
